Despite the remarkable performance of supervised medical image segmentation models, relying on a large amount of labeled data is impractical in real-world situations. Semi-supervised learning approaches aim to alleviate this challenge using unlabeled data through pseudo-label generation. Yet, existing semi-supervised segmentation methods still suffer from noisy pseudo-labels and insufficient supervision within the feature space. To solve these challenges, this paper proposes a novel semi-supervised 3D medical image segmentation framework based on a dual-network architecture. Specifically, we investigate a Cross Consistency Enhancement module using both cross pseudo and entropy-filtered supervision to reduce the noisy pseudo-labels, while we design a dynamic weighting strategy to adjust the contributions of pseudo-labels using an uncertainty-aware mechanism (i.e., Kullback-Leibler divergence). In addition, we use a self-supervised contrastive learning mechanism to align uncertain voxel features with reliable class prototypes by effectively differentiating between trustworthy and uncertain predictions, thus reducing prediction uncertainty. Extensive experiments are conducted on three 3D segmentation datasets, Left Atrial, NIH Pancreas and BraTS-2019. The proposed approach consistently exhibits superior performance across various settings (e.g., 89.95\% Dice score on left Atrial with 10\% labeled data) compared to the state-of-the-art methods. Furthermore, the usefulness of the proposed modules is further validated via ablation experiments.